of a strong argument may be just as subjective given it is a based on a person's opinion. I am not saying that you do or don't have a strong argument for either school (assuming the ACC and/or Big Ten were interested in either or both).

Based on what I know about both schools' athletic programs and the reasons given to justify past decisions (including Army's experiment as a football-only member in C-USA), I do believe there is a possibility that you may have an easier time convincing Notre Dame to join the ACC as a football member than convincing Army and Navy to agree with your proposal. If you want to increase your odds of success, then you may have to provide other options (i.e. football-only membership and both could join the same conference) on the negotiation table. Once they get used to football in the ACC, then you could always go back to them and ask if they would be opening to joining the ACC in lacrosse too. Basically slow play the idea of full membership by getting them to say 'yes' to sports both schools could do well in from the start.